cp's OEIS Frontend

A120164 a(n) = 6 + floor( Sum_{j=1..n-1} a(j)/4 ).

%I A120164 #7 Sep 06 2023 01:33:47
%S A120164 6,7,9,11,14,17,22,27,34,42,53,66,83,103,129,161,202,252,315,394,492,
%T A120164 615,769,961,1202,1502,1878,2347,2934,3667,4584,5730,7163,8953,11192,
%U A120164 13990,17487,21859,27324,34155
%N A120164 a(n) = 6 + floor( Sum_{j=1..n-1} a(j)/4 ).
%H A120164 G. C. Greubel, <a href="/A120164/b120164.txt">Table of n, a(n) for n = 1..1000</a>
%t A120164 f[n_, p_, q_]:= f[n, p, q]= p +Quotient[q +Sum[f[k,p,q], {k,n-1}], 4];
%t A120164 A120164[n_]:= f[n,6,0];
%t A120164 Table[A120164[n], {n, 60}] (* _G. C. Greubel_, Sep 05 2023 *)
%o A120164 (Magma)
%o A120164 function f(n, a, b)
%o A120164   t:=0;
%o A120164     for k in [1..n-1] do
%o A120164       t+:= a+Floor((b+t)/4);
%o A120164     end for;
%o A120164   return t;
%o A120164 end function;
%o A120164 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120164 A120164:= func< n | g(n, 6, 0) >;
%o A120164 [A120164(n): n in [1..60]]; // _G. C. Greubel_, Sep 05 2023
%o A120164 (SageMath)
%o A120164 @CachedFunction
%o A120164 def f(n,p,q): return p + (q +sum(f(k,p,q) for k in range(1, n)))//4
%o A120164 def A120164(n): return f(n, 6, 0)
%o A120164 [A120164(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 05 2023
%Y A120164 Cf. A072493, A073941, A112088.
%K A120164 nonn
%O A120164 1,1
%A A120164 _Graeme McRae_, Jun 10 2006